It's not true word by word, but the general idea is the same. Elves and gnomes came from the Feywild/Faerie and were originally Fey, but lost most of their Feyness over time.
The nature of the Feywild and the Fey are left very hazy because they need to cover a lot of concepts, from literal nature spirits like dryads nymphs to pint-sized winged Tinklebells and other trickster spirits to regal Mabs and Gentlemen With Thistledown Hair and Tom Bombadills. Fey are generally very undefined creatures in folklore, you won't find any easily categorified definition there beyond "you better not mess with them or they will mess you back something fierce -- actually they may still do that anyway so it's better to just not be noticed by them at all".
